The VLA Frontier Field Survey: A Comparison of the Radio and UV/optical size of $0.3 \lesssim z \lesssim 3$ star-forming galaxies

To investigate the growth history of galaxies, we measure the rest-frame radio, ultraviolet (UV), and optical sizes of 98 radio-selected, star-forming galaxies (SFGs) distributed over $0.3 \lesssim z \lesssim 3$ and median stellar mass of $\log(M_\star/ \rm M_\odot)\approx10.4$. We compare the size of galaxy stellar disks, traced by rest-frame optical emission, relative to the overall extent of star formation activity that is traced by radio continuum emission. Galaxies in our sample are identified in three Hubble Frontier Fields: MACSJ0416.1$-$2403, MACSJ0717.5+3745, and MACSJ1149.5+2223. Radio continuum sizes are derived from 3 GHz and 6 GHz radio images ($\lesssim 0$''$.6$ resolution, $\approx0.9\, \rm \mu Jy\, beam^{-1}$ noise level) from the Karl G. Jansky Very Large Array. Rest-frame UV and optical sizes are derived using observations from the Hubble Space Telescope and the ACS and WFC3 instruments. We find no clear dependence between the 3 GHz radio size and stellar mass of SFGs, which contrasts with the positive correlation between the UV/optical size and stellar mass of galaxies. Focusing on SFGs with $\log(M_\star/\rm M_\odot)>10$, we find that the radio/UV/optical emission tends to be more compact in galaxies with high star-formation rates ($\rm SFR\gtrsim 100\,M_\odot\,yr^{-1}$), suggesting that a central, compact starburst (and/or an Active Galactic Nucleus) resides in the most luminous galaxies of our sample. We also find that the physical radio/UV/optical size of radio-selected SFGs with $\log(M_\star/\rm M_\odot)>10$ increases by a factor of $1.5-2$ from $z\approx 3$ to $z\approx0.3$, yet the radio emission remains two-to-three times more compact than that from the UV/optical. These findings indicate that these massive, {radio-selected} SFGs at $0.3 \lesssim z \lesssim 3$ tend to harbor centrally enhanced star formation activity relative to their outer-disks.